Vibration Serviceability Analysis Of Aluminum Pedestrian .
6th International Conference on Advances in Experimental Structural Engineering11th International Workshop on Advanced Smart Materials and Smart Structures TechnologyAugust 1-2, 2015, University of Illinois, Urbana-Champaign, United StatesVibration Serviceability Analysis of Aluminum Pedestrian BridgesSubjected to Crowd LoadingP. Dey1, S. Walbridge2, S. Narasimhan31PhD Student, Dept. of Civil and Environmental Engineering, University of Waterloo, Waterloo, Canada.E-mail: pdey@uwaterloo.ca2 Associate Professor, Dept. of Civil and Environmental Engineering, University of Waterloo, Waterloo, Canada.E-mail: swalbridge@uwaterloo.ca3 Associate Professor, Dept. of Civil and Environmental Engineering, University of Waterloo, Waterloo, Canada.E-mail: sriram.narasimhan@uwaterloo.caABSTRACTUse of aluminum as material for pedestrian bridges is increasingly becoming popular due to its highstrength-to-weight ratio and reduced susceptibility to corrosion during the service life of the bridge. However,these structures have low intrinsic damping and mass. As a result, they tend to be lively under operational loadsand often exhibit large amplitude vibrations. Controlling the excessive vibration response and assessing theserviceability are the main design criteria for pedestrian bridges. Different codes of practice have been developedby different countries to assess the vibration serviceability of pedestrian bridges based on simplified models ofpedestrian induced walking load. Two general approaches are mainly followed in different guidelines to designpedestrian bridges for vibration serviceability. The first approach focuses on avoiding natural frequencies of thestructure that coincide with the normal walking frequency range. The second approach is to limit the vibrationresponse in terms of the predicted acceleration within the desired comfort limit. This paper presentsserviceability assessment of two full scale aluminium pedestrian bridges with different vibration characteristics.The natural frequencies of the bridges create near resonant conditions with the first as well as the higherharmonics of walking frequencies. Crowd testing was performed on the two bridges with different crowddensities and measurements of accelerations were recorded at three different locations along the bridge span inboth vertical and lateral directions. The comfort-based evaluations of the two bridges were performed bycomparing the measurements with the predicted and the acceptable limits of vibrations as recommended incodes and several guidelines. The present study demonstrates that the current codes and guidelines are not fullyapplicable to all kinds of pedestrian bridges, specifically for bridges with resonance in higher harmonics ofwalking. Also the study has shown extensive inconsistency in predicted responses by the guidelines. It isrecommended that the current guidelines should account for resonance in higher harmonics of walking. Furtherexperimental study is recommended on full scale pedestrian bridges with different dynamic characteristics toinvestigate the applicability of these guidelines for different kinds of footbridges.KEYWORDS: Pedestrian bridges, serviceability, design guidelines, crowd load1. INTRODUCTIONIn recent years, serviceability of lightweight and slender pedestrian bridges has been the focus of manyresearchers. Due to their low mass and stiffness, these structures have natural modes, which often coincide withthe human walking frequencies. As a result, these footbridges tend to suffer high amplitude vibrations leading toserviceability issues. Some of the famous incidents of serviceability failures of pedestrian bridges include theLondon Millennium footbridge (LMF) [1], the Pont du Solferino in Paris [2] and the T-Bridge, Japan [3]. Theprimary cause of these high profile incidents was excessive vibration under resonance with walking frequenciesof the pedestrians. In design codes, the serviceability problems are considered by giving limits to the structuralvibration modes to avoid resonance. These frequency limits are known as critical frequencies. If the naturalvibration modes of a structure fall within these critical ranges, the serviceability of these structures is ensured bylimiting the level of vibration under the human induced excitations within acceptable values. The acceptablelimits of vibrations are decided based on experiments and experiences on human perception to vibration level.While pedestrians are relatively insensitive to low amplitude vibrations in the vertical direction of bridgeoscillation, a small level of lateral oscillation can affect walking behaviour. Various codes and guidelines haveproposed limits related to lateral vibrations, but they are not consistent with each other [4].
It is expected that bridge vibrations are often enhanced by groups of pedestrians or continuous crowds ascompared to single pedestrian loading. Hence it is important to consider design loads from multiple trafficscenarios in assessing serviceability of pedestrian bridges. After the high profile incident of LMF, a fewguidelines [5-8] focused on crowd loading and corresponding synchronous vibration of pedestrian bridges.Although multiple simplified design methodologies have been developed to incorporate crowd effects, there isstill a need to validate these guidelines for different bridge types. To the authors’ knowledge, these guidelineshave not been applied to aluminum pedestrian bridges. The main objective of this study is to assess severaldesign guidelines [5-8] for assessing vibration serviceability of aluminum pedestrian bridges.In the current study, experiments have been performed to investigate the dynamic behaviour of two aluminumbridges under crowd loading. The bridges have the same cross sectional and material properties but differentspans. Due to its high strength-to-weight ratio, and the benefits over other metals in terms of life cycle cost,aluminum is increasingly being considered for use in bridge applications. However, no attention has been giventowards the serviceability study of aluminum pedestrian bridge while these structures may experience severeserviceability issues under certain loading scenarios. The current study focuses in verifying the applicability ofthe current design guidelines for aluminum pedestrian bridges under crowd excitation.2. DESCRIPTION OF EXPERIMENTS2.1. The Testing PlatformTwo aluminum pedestrian bridges of spans 12.2 m and 22.9 m, respectively, were studied. They wereconstructed solely for research purposes in the Structural Laboratory of University of Waterloo, Canada. Thebridges were assembled with bolted connections from a patented modular product called Make-A-Bridge byMAADI Group. The extruded members were T-6061 aluminum. Both specimens were 1.35 m in width and1.140 m in height with identical cross sectional properties. The bridge can be constructed with or without lateralcross-bracing under the deck to vary the lateral stiffness. In this paper, results are presented for the case of nolateral cross-bracing modelling a bridge that is relatively soft, laterally. More details of the modular bridgespecimens are presented elsewhere (Dey et al. [9]). The bridge specimens and one of the typical bolted joints areshown in Fig. 2.1. The 12.2 m and 22.9 m bridges weighed respectively 982 kg and 1,735 kg.Figure 2.1 (a) Bridge specimen of span 12.2 m (b) Bridge specimen of span 22.9 m [9] (c) Typical bolted joint[9]In order to measure the accelerations of the structures, the pedestrian bridges were instrumented with twelvelow-frequency, high-sensitivity accelerometers, which have operable frequency range of 0.1 Hz to 200 Hz. Theaccelerometers were placed on the bottom chords at quarter and mid-points along the length, both laterally andvertically using aluminum mounting blocks. The acceleration data were recorded using three 4-channel A/D dataacquisition modules (daisy-chained); model DT9837A manufactured by Data Translation.Prior to conducting walking tests on the pedestrian bridges, set of modal tests were performed to estimate the
dynamic properties of the structures. A description of the tests and methodology to estimate the correspondingmodal properties, which are used in this paper for the crowd loading analysis, is provided in a recent work byDey et al. [9], The estimated modal natural frequencies and damping are listed in Table 2.1Table 2.1 First modal frequencies and damping of the pedestrian bridgesLateralVerticalBridge specimensNaturalNatural FrequencyDamping RatioDamping Ratiofrequency(Hz)(Hz)12.2 m2.30.25011.80.01222.9 m1.20.0124.50.0082.2 Crowd TestA set of pedestrian walking tests were performed on the two bridges including single as well as groups ofpedestrians. The current study focuses only on the tests under multiple pedestrians. The tests conducted on thetwo bridges involved two people walking synchronously and asynchronously, and walking of groups ofpedestrians with varying densities. Table 2.2 reports the number of pedestrians involved in different tests andcorresponding average mass of the crowd crossing the bridge. For statistical significance, the crowd tests on the12.2 m bridge specimen were repeated 30 times while 10 trials were conducted for each set of tests for the22.9 m specimen. During the tests, the pedestrians were asked to walk at a normal pace to generate randomcrowd loading on the bridges. Fig. 2.2 shows several pictures of the crowd tests on the bridges.No1234567Table 2.2 Test matrix for the two bridges12.2 m pedestrian bridge22.9 m pedestrian bridgeStandardAveragedeviationAverageDescription of testsDescription of testsmass (kg)of massmass (kg)(kg)2 persons walking2 persons walking66.52.167.5synchronouslysynchronously2 persons walking2 persons walking66.52.167.5asynchronouslyasynchronously4 persons or 0.2 p/m269144 persons or 0.1 p/m26528 persons or 0.5 p/m6796 persons or 0.2 p/m27217 persons or 1.0 p/m2681410 persons or 0.3 p/m270------------15 persons or 0.5 p/m271------------22 persons or 0.7 p/m268Figure 2.2 Crowd tests on the 12.2 m (left) and 22.9 m (right) bridge specimensStandarddeviationof mass(kg)11.611.64.17.511.810.812.4
3. OVERVIEW OF DESIGN GUIDELINES ON PEDESTRIAN BRIDGESThere are only few guidelines [5-8], which have incorporated the effect of crowd on the serviceability ofpedestrian bridges. Although these guidelines are based on different assumptions and approaches to consider thecrowd effect in the bridge and corresponding response predictions, they evaluate the serviceability of thepedestrian bridges through two main steps. The first step involves limiting the structural frequencies to thoseoutside a critical frequency range (Table 3.1). When the natural frequencies of the structures are outside therange, they automatically satisfy the maximum comfort level for the occupants. On the other hand, if thefrequencies fall within the critical range, the second step of the design methodology is followed. In this step, adetailed dynamic analysis has to be performed and the predicted vibration level should be within the acceptablelimit of vibration in accordance to the guideline. These acceptable limits are given in the design guidelines andthere is generally no consensus on these limits. As these limits are based on human perception, which may varybetween individuals, these limits are by themselves highly uncertain. However, current guidelines haveproposed deterministic values of these limits based on past experiences and experiments. Table 3.1 describes thecritical frequency ranges and the acceptable limits according to different guidelines.Table 3.1 Critical frequencies and acceptable limits of vibration by current guidelinesCodesLimit Acceleration (m/s2)Critical Frequencies (Hz)VerticalLateralVerticalLateralEurocode 5 5 2.50.700.4British National Annex toEurocode 1 8 1.52.0 (upper bound)--SÉTRA1-50.3-2.51.0 (mean)0.3 (mean)HIVOSS1.25-4.60.5-1.21.0 (mean)0.3 (mean)3.1. Methodologies for Dynamic AnalysisIn order to evaluate the vibration level under crowd excitations, dynamic response analysis has to be performed.The guidelines, mentioned in Table 3.1, have considered various modeling approaches of human induced loadsand corresponding calculation methodologies for dynamic response. While, Eurocode 5 [5] has proposed directequations for response predictions, the British National Annex [6], the French guideline SÉTRA [7] and theEuropean guideline HIVOSS [8] have characterized the pedestrian loading under crowd conditions andpredicted the response either through the SDOF approach or finite element analysis.The Eurocode 5 has been developed to estimate acceleration response under several persons walking on a timberpedestrian bridge. As the methodology is not material dependent, it has been applied for aluminum bridges in thecurrent study. For n persons crossing the bridge, the vertical and lateral accelerations of the bridge can beestimated respectively through the following two equations:𝑎𝑣,𝑛 0.23𝑎𝑣,1 𝑛𝑘𝑣𝑒𝑟𝑡𝑎ℎ,𝑛 0.18 𝑎ℎ,1 𝑛𝑘ℎ𝑜𝑟(3.1)(3.2)where, av,1 is the vertical response under one individual walking, which is given by:200𝑀𝜉𝑎𝑣,1 {100𝑀𝜉, for 0 𝑓𝑣 2.5, for 2.5 𝑓𝑣 5.0(3.3)ah,1 is the lateral response under one individual walking, which is given by:𝑎ℎ,1 50𝑀𝜉, 0.5 𝑓ℎ 2.5(3.4)In the above equations, M and ξ are the mass and damping of the structure and the factors, kvert and khor, depend onthe vertical and lateral structural frequencies, kv and kh.
The British National Annex to Eurocode 1 has proposed different load models in the vertical direction based oneither pedestrians walking in a group together or continuous traffic uniformly distributed over the bridge deckarea. However, this guideline has not proposed any dynamic response analysis in the lateral direction. It justrequires checking of the stability of the structure in the lateral direction through a damping parameter dependingonly on the pedestrian and the structure mass along with the structure damping. The vertical moving load,applied on the bridge under n pedestrians crossing the bridge together, is given by:𝐹 (0.4𝐺)𝑘(𝑓𝑣 ) 1 𝛾(𝑛 1) sin(2𝜋𝑓𝑣 𝑡)(3.5)where, G is the pedestrian weight, k(fv) is combined factor as a function of vertical natural frequency of fv, and γ isa factor to allow for the unsynchronised combination of pedestrian actions depending on the damping of thestructure. For the continuous crowd scenario, where steady state is achieved, the applied load is distributed overthe area, which is given by:𝑤 1.8(0.4𝐺)𝐴𝑘(𝑓𝑣 ) 𝛾𝑛𝜆sin(2𝜋𝑓𝑣 𝑡)(3.6)In the above equation, λ is the factor that reduces the effective number of pedestrian in proportion to the enclosedarea of the mode of interest and equals to 0.634 for the first mode shape of a simply supported beam.The French SÉTRA and the European HIVOSS guidelines have a similar approach to predict pedestrian bridgeresponses. They only differ in considering the effect of additional mass from crowd in the response calculations.While HIVOSS incorporates the additional mass effect if it crosses more than 5% the modal mass of thepedestrian bridge, the SÉTRA guideline does not have any limitations on this parameter. The SÉTRA guidelineestimates two different bounds of responses considering structural frequencies of the empty structure and thestructure with the occupied pedestrians. For the current study, the HIVOSS guideline has not been consideredfor response predictions due to its similarity with the SÉTRA guideline. The SÉTRA guideline specifies fourdifferent classes of bridges with five different traffic classes. The random load due to a stream of n pedestrianscorresponding to a specific crowd density (d p/m2) is simplified to an equivalent number of pedestrians (neq),which are uniformly distributed over the bridge deck, i.e.:𝑛𝑒𝑞 {10.8 𝑛𝜉, 𝑓𝑜𝑟 𝑑 1.01.85 𝑛, 𝑓𝑜𝑟 𝑑 1.0(3.7)The magnitude of distributed load per area (A) in any direction (vertical or lateral) is defined as:𝑝 𝛼𝐺𝜓𝑛𝑒𝑞𝐴(3.8)In the above equation, α is the dynamic load factor and is 0.4 and 0.1 for the first and second harmonics in thevertical direction. It has values of 0.05 and 0.01 for, respectively, the first and second harmonics in the lateraldirection. Ψ is the reduction factor and is a function of structural frequency.In the current study, as both the bridges were simply supported and can be assumed to behave as simplysupported beams, the resonant maximum acceleration under the load models from the British National Annexand the SÉTRA guideline can be estimated through the SDOF approach, which is given by:𝑃𝑚𝑚 𝑀𝑚𝑎𝑚 2𝜉(3.9)Here, Pm, Mm and ξm are the generalized (modal) load, mass and damping ratio of the structure. For a distributedload p per unit length, the generalized load is given by 2pL/π for first mode of vibration and is half for thesecond mode of vibration. Similarly, the modal load for moving load F for any mode is 2F/π.4. EVALUATION OF SEVICEABILITYIn this section, serviceability of the two bridges under different crowd scenarios is evaluated according to thedesign guidelines listed in Table 3.1 (except HIVOSS). Firstly, the fundamental frequencies of the bridges in bothvertical and lateral direction are compared with the critical ranges of frequencies. If the natural frequencies fall
within this range, the second step of the assessment is performed, otherwise it is assumed that the structuresautomatically satisfy the comfort limits as proposed by the corresponding guideline.4.1. Evaluation through Frequency CriteriaThe 12.2 m bridge specimen has its fundamental lateral frequency at 2.3 Hz while the first vertical frequency is11.81 Hz. According to Table 3.1, the pedestrian bridge automatically satisfies the maximum comfort level asthe vertical frequency is outside the critical range. Thus, further analysis is not required in this direction.However, the lateral frequency lies within the critical range according to Eurocode 5 and the SÉTRA guidelineand thus, dynamic analysis needs to be performed in lateral direction to evaluate its serviceability. A similarevaluation has also been conducted for the 22.9 m bridge specimen with lateral and vertical frequencies being1.2 Hz and 4.5 Hz, respectively. All of the codes recommend dynamic evaluation of vibration to assess theserviceability in both the directions for this structure. In the following section, the dynamic analysis of thepedestrian bridges has been performed under crowd excitation and the maximum predicted and measuredresponses are compared with the limits to assess the serviceability.4.2. Evaluation of Vibration level to Crowd ExcitationEurocode 5 has suggested predicting the peak acceleration of the pedestrian bridges under crowd excitationthrough the application of the direct equations (Eq. 3.1 and Eq. 3.2). The British National Annex and SÉTRAguidelines apply the load models as proposed on the pedestrian bridges and estimate peak acceleration through theSDOF approach (Eq. 3.9). The maximum acceleration occurred at the mid-point of the bridge spans in all cases.Hence only the peak measurements at the centre of the bridges have been considered for this study. The results ofthe serviceability assessment under different pedestrian loading scenarios are plotted in Figure 4.1 for both thepedestrian bridges in the vertical as well as the lateral direction.120.8(a)1.50.610.42Peak Acceleration (m/s )(b)0.50.2002PSync2PAsync0.22p/m0.51.022p/m �TRA(empty)SÉTRA(occupied)MeasurementBritish NationalAnnexEurocode 5limit byBritish NationalAnnexlimit byEurocode 5limit by Setra(d)1.5150.502 P 2 P 4 P 0.2 0.3 0.5 0.72222Sync Asyncp/m p/m p/m p/m02 P 2 P 4 P 0.2 0.3 0.5 0.72222Sync Asyncp/m p/m p/m p/mFigure 4.1 (a) Comparison of measured and predicted peak acceleration with acceptable limits for (a) the 12.2 mpedestrian bridge in vertical direction, (b) the 12.2 m pedestrian bridge in lateral direction, (c) the 22.9 mpedestrian bridge in vertical direction, and (d) the 22.9 m pedestrian bridge in lateral direction (here ‘P’ standsfor pedestrian)As discussed in the previous section, the 12.2 m bridge specimen is safe in terms of serviceability and no dynamicanalysis is required according to all of the codes. Despite this fact, the measured maximum acceleration of thepedestrian bridges under different traffic scenario are compared with the acceptable vibration limits in Fig. 4.1 (a)and it is observed that the measurements have crossed the limits specified by Eurocode 5 and the SÉTRAguideline. During the two pedestrian walking case, the pedestrians were walking in their normal walking pace,
which is near 2 Hz. It is expected that the higher level of vibration might result from a near resonant condition withthe sixth harmonics of the walking frequency. Similarly, for a denser crowd (1.0 p/m2), the speed of walkingbecome slow and sometimes, the structural frequency of 11.8 Hz may have near resonant condition with theseventh harmonic of the slow walking frequency (1.67 Hz), and thus generates a higher level of vibration.In the lateral direction, the design guidelines have underestimated the measurements (Fig. 4.1 (b)). Thepredictions have not indicated any serviceability issue although measurements have crossed the limit valuesduring all loading scenarios. The significant lower predictions might be due to the measured high damping values(20%) in the structures. None of the guidelines specify any damping values for aluminum alloys, although thecodes suggest a damping of as low as 0.4% -1% for metals like steel. As the damping of a structure depends on thefixity of connections, support condition and friction between structural and non-structural components, the highvalue of damping is not surprising. However, in reality the actual damping of structures is not known at the designstage and it is common practice to assume the damping values suggested in the codes. It is obvious that a lowervalue of damping will increase the predictions. It will be interesting to see in future study the sensitivity of thesepredictions to the effect of damping uncertainty, which is not in the scope of the current work.Through the evaluation of the frequency criteria, dynamic analysis has to be performed for the 22.9 m bridgespecimen in both the directions. Fig. 4.1(c) and Fig. 4.1(d) show the serviceability assessment of the bridgespecimen in the vertical and lateral directions respectively. It is observed that the predictions are overestimatingthe measurements in the vertical direction. The peak measurements under any loading scenario has crossed thelimits defined by the SÉTRA guideline and the Eurocode 5, leading to a serviceability issue, although themeasurements are safe according to the upper limit of the British National Annex. Only denser traffic leads to aserviceability issue according the British National Annex. However, all the predictions are over the limits and leadto a very conservative design scenario. It is worth mentioning that the vertical mode of the bridge (4.5 Hz) fallswithin the second harmonic of the walking frequency range and thus has a chance of resonating with the fasterwalking speed. As all the codes consider resonance up to the second harmonic, and overestimate the response inresonant condition [12], the predictions are very high as compared to the measurements.Similar to the 12.2 m bridge specimen, the predictions are underestimated in lateral direction for the 22.9 mbridges specimen, although the SÉTRA guideline reports a serviceability issue under denser crowd loading likethe measurements. In any case of crowd loading, the Eurocode 5 predicts a very low vibration level below thelimits. As mentioned earlier, the estimated high damping might be one of the reasons behind these low predictionsfor the 22.9 m bridge specimen. Further study is recommended, however, to confirm this.5. CONCLUSIONSIn this study, serviceability assessment of two full scale aluminum pedestrian bridges has been performed inaccordance with three design guidelines, namely: Eurocode 5, the British national Annex to Eurocode 1 and theFrench SÉTRA guideline, under different crowd loading cases. A suite of tests was conducted on these twobridges with different groups of pedestrians crossing each structure. The oscillations of the bridges weremeasured in terms of the acceleration parameter at different locations on the bridges. Firstly, the structuralfrequencies in the vertical as well as the lateral directions were verified with the critical ones to decide upon therequirement of dynamic analysis of the bridges. Except for the 12.2 m bridge specimens in the vertical direction,peak responses to crowd loading had to be compared with the acceptable limits to assess the correspondingserviceability. An important conclusion of the experimental investigation is that resonance with higher thansecond harmonics can cause serviceability issues. It is recommended to investigate in the future the maximumnumbers of harmonics that should be incorporated in the design for serviceability. The peak responses in thevertical direction for the 22.9 m bridge specimen are also in agreement with the previously found fact that thecodes of practices overestimate the response in the resonant scenario. As damping is one of the importantparameters, along with structural vibration frequency, in designing for serviceability, it is suggested that theeffect of damping on the predictions by different guidelines should be further explored.AKCNOWLEDGEMENTThe authors want to acknowledge the financial support provided by the Natural Sciences Engineering ResearchCouncil of Canada (NSERC) through the Collaborative Research Grants (CRD) program. The authors aregrateful to the industry contributions, provided by the Aluminum Association of Canada (AAC) and MAADIGroup. The authors also want to thank Dr. Arndt Goldack from TU-Berlin for his useful suggestions during the
experimental program and for assisting with the walking tests for the longer span structure. The help with thetest setup provided by Ann Sychterz, Richard Morrison, and Rob Sluban is also gratefully acknowledged.Finally, the authors want to thank all the volunteers involved in the numerous walking tests.REFERENCES1.Dallard, P., Fitzpatrick, and T., Flint, A., et al. (2001). London Millennium Bridge: pedestrian-inducedlateral vibration. Journal of Bridge Engineering. 6(6), 412-417.2. Danbon, F. and Grillaud, F. (2005). Dynamic behaviour of a steel footbridge. Characterization and modelingof the dynamic loading induced by a moving crowd on the Solferino footbridge in Paris. Proceedings ofFootbridge 2005. Venice, Italy.3. Fujino, Y., Pacheco, B., Nakamura, S., and Warnitchai, P. (1993). Synchronization of human walkingobserved during lateral vibration of a congested pedestrian bridge. Earthquake engineering & structuraldynamics. 22(9), 741-758.4. Zivanovic, S., Pavic, A., and Reynolds, P. (2005). Vibration serviceability of footbridges underhuman-induced excitation: a literature review. Journal of sound and vibration. 279(1), 1-74.5. BS NA EN 1991-2 (2003). UK National Annex to Eurocode 1: Actions on structures- Part 2: Traffic loadson bridges. British Standards.6. EN 1995-2 (2004). Design of timber structures - part 2: Bridges. European Committee of Standardization,Eurocode 5.7. HIVOSS (2008) ‘Design of Footbridges Guideline: Human Induced Vibrations of Steel Structures.RFS2-CT-2007-00033.8. SÉTRA (2006). Assessment of vibrational behaviour of footbridges under pedestrian loading.Technicalguide SÉTRA, Paris, France.9. Dey, P., Sychterz, A., and Narasimhan, S., Walbridge, S. (2015). Performance of pedestrian-load modelsthrough experimental studies on lightweight aluminum bridges. Journal of Bridge Engineering, ASCE,(Accepted).10. Caprani, C. C., Keogh, J., Archbold, P., & Fanning, P. (2012). Enhancement factors for the verticalresponse of footbridges subjected to stochastic crowd loading. Computers & Structures, 102, 87-96.
serviceability are the main design criteria for pedestrian bridges. Different codes of practice have been developed by different countries to assess the vibration serviceability of pedestrian bridges based on simplified models of pedestrian induced walking load. Two general approaches are mainly fo
The vibration analysis in Section 5 provides the FE-based vibration analysis procedure based on first principles direct calculations. The FE-based vibration analysis is recommended to evaluate the design during the detail design stage. If found necessary, the local vibration is tobe addressed in the detail vibration analysis. The
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